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Two circles have a 24-cm common chord, their centers are 14 cm apart, and the radius of one of the circles is 13 cm. Make an accurate drawing, and find the radius for the second circle in your diagram. There are two solutions; find both.

I was able to find one of the two measure of the radius, which is 15cm, by drawing a large circle and smaller circle. I assumed that the radius of the smaller circle would be 13cm and using the Pythagorean Theorem, I got to the calculation of 15cm to be the radius of the large circle. I am not sure of how I can find the second possible measure of the radius, therefore, any help I receive will be highly appreciated.

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Hint: The second solution should be by having the center of the smaller circle inside the larger one, instead of outside, something like the figure below (ignore the numbers on the figure) The radius of the smaller circle in the figure should be 13cm (the radius of the larger circle should obviously be larger than the distance between centers, which is 14cm):

enter image description here

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enter image description here enter image description here

$|O_1O_2|=d=14$, $|O_1A|=|O_1B|=r_1=13$, $|O_2A|=|O_2B|=r_2$, $|AB|=h=24$.

\begin{align} r_2&=\sqrt{\tfrac{h^2}4+\left(d\pm\sqrt{r_1^2-\tfrac{h^2}4}\right)^2} =\sqrt{r_1^2+d^2\pm d\,\sqrt{4\,r_1^2-h^2}} \tag{a}\label{a} , \end{align}

two values for $r_{2}$ are 15 and $\sqrt{505}\approx22.4722$.

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